Related papers: Dehn surgeries and negative-definite four-manifold…
Kreck's modified surgery theory reduces the classification of closed, connected 4-manifolds, up to connect sum with some number of copies of $S^2\times S^2$, to a series of bordism questions. We implement this in the case of unorientable…
The Heegaard Floer correction term ($d$-invariant) is an invariant of rational homology 3-spheres equipped with a Spin$^c$ structure. In particular, the correction term of 1-surgeries along knots in $S^3$ is a ($2\mathbb{Z}$-valued) knot…
We calculate the RT-invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [V. G. Turaev, Quantum invariants of knots and 3--manifolds, de…
By considering negative surgeries on a knot $K$ in $S^3$, we derive a lower bound to the non-orientable slice genus $\gamma_4(K)$ in terms of the signature $\sigma(K)$ and the concordance invariants $V_i(\overline{K})$, which strengthens a…
We give a survey of geometric approaches to the topological 4-dimensional surgery and 5-dimensional s-cobordism conjectures, with a focus on the study of surfaces in 4-manifolds. The geometric lemma underlying these conjectures is a…
We generalize the Manolescu-Owens smooth concordance invariant delta(K) of knots K in the 3-sphere to invariants delta_{p^n}(K) obtained by considering covers of order p^n, with p prime. Our main result shows that for any odd prime p, the…
We study which closed, connected, orientable three-manifolds $X$ containing a Klein bottle arise as integral Dehn surgery along a knot in $S^3$. Such $X$ are presentable as a gluing of the twisted $I$-bundle over the Klein bottle to a knot…
In an earlier paper, we used the absolute grading on Heegaard Floer homology to give restrictions on knots in $S^3$ which admit lens space surgeries. The aim of the present article is to exhibit stronger restrictions on such knots, arising…
Kashaev's invariants for a knot in a three sphere are generalized to invariants of a knot in a three manifold. A relation between the newly constructed invariants and the hyperbolic volume of the knot complement is observed for some knots…
We extend the construction of upsilon-type invariants to null-homologous knots in rational homology three-spheres. By considering $m$-fold cyclic branched covers with $m$ a prime power, this extension provides new knot concordance…
We study three knot invariants related to smoothly immersed disks in the four-ball. These are the four-ball crossing number, which is the minimal number of normal double points of such a disk bounded by a given knot; the slicing number,…
We introduce new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union of two identical surfaces. The invariants are constructed via surgery on manifolds of the form $F \times I$…
We study the Yamabe invariant of manifolds obtained as connected sums along submanifolds of codimension greater than 2. In particular, given a compact smooth manifold M which does not admit metrics of positive scalar curvature, we prove…
A pair of Dehn surgeries on a knot is called chirally cosmetic if they yield orientation-reversingly homeomorphic 3-manifolds. In this paper, we consider exceptional or half-integral chirally cosmetic surgeries, and obtain several…
In this paper we study submanifold with nonpositive extrinsic curvature in a positively curved manifold. Among other things we prove that, if $K\subset (S^n, g)$ is a totally geodesic submanifold in a Riemannian sphere with positive…
The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of…
We study torus knot invariants in the lens space $S^{3}/\mathbb{Z}_{p}$ within Chern--Simons theory. Using the surgery and modular description of lens spaces, we derive a general expression for the invariant of an $(\alpha,\beta)$ torus…
We will classify all exceptional Dehn surgeries on 2-bridge knots according to whether they produce reducible, toroidal, or small Seifert fibered manifolds.
Previous work of the authors establishes a criterion on the fundamental group of a knot complement that determines when Dehn surgery on the knot will have a fundamental group that is not left-orderable. We provide a refinement of this…
It is conjectured that a hyperbolic knot admits at most three Dehn surgeries which yield closed three manifolds containing incompressible tori. We show that there exist infinitely many hyperbolic knots which attain the conjectural maximum…